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Search: id:A144270
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| A144270 |
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Lower triangular array called S2hat(-1) related to partition number array A144269. |
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6
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| 1, 1, 1, 3, 1, 1, 15, 4, 1, 1, 105, 18, 4, 1, 1, 945, 129, 19, 4, 1, 1, 10395, 1095, 132, 19, 4, 1, 1, 135135, 11880, 1119, 133, 19, 4, 1, 1, 2027025, 149940, 12057, 1122, 133, 19, 4, 1, 1, 34459425, 2218545, 151560, 12081, 1123, 133, 19, 4, 1, 1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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If in the partition array M32hat(-1)=A144269 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-1). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
The first three columns are A001147, A144272, A144273.
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REFERENCES
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W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, preprint Oct 2008.
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LINKS
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W. Lang, First 10 rows of the array and more.
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FORMULA
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a(n,m)=sum(product(|S2(-1;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S2(-1;j,1)|= A001497(j-1,0) = A001147(j-1) = (2*j-3)(!^2) (2-factorials) for j>=2 and 1 if j=1.
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EXAMPLE
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[1];[1,1];[3,1,1];[15,4,1,1];[105,18,4,1,1];...
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CROSSREFS
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Row sums A144271.
Sequence in context: A006956 A072285 A144269 this_sequence A110112 A156690 A060325
Adjacent sequences: A144267 A144268 A144269 this_sequence A144271 A144272 A144273
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 09 2008
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EXTENSIONS
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First %C line: changed M32khat(-1) into M32hat(-1)=A144269.%e line: chabged [15,4,1] into [15,4,1,1]. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 28 2008
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